Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DMaximumAverageSets solver = new DMaximumAverageSets();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMaximumAverageSets {
        long[][] ncr;

        private long ncr(int n, int r) {
            if (r > n || r < 0) return 0;
            return ncr[n][r];
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();

            ncr = new long[n + 1][n + 1];
            ncr[0][0] = 1;

            for (int i = 0; i < n; i++) {
                for (int j = 0; j <= i; j++) {
                    ncr[i + 1][j] += ncr[i][j];
                    ncr[i + 1][j + 1] += ncr[i][j];
                }
            }

            int a = in.nextInt(), b = in.nextInt();

            long[] v = new long[n];
            for (int i = 0; i < n; i++) {
                v[i] = in.nextLong();
            }

            Arrays.sort(v);

            double sum = 0;
            for (int i = n - 1; i >= n - a; i--) {
                sum += v[i];
            }

            long lastElement = v[n - a];
            int count1 = 0, count2 = 0;
            for (int i = 0; i < n; i++) {
                if (v[i] == lastElement) {
                    if (i >= n - a) {
                        count1++;
                    } else {
                        count2++;
                    }
                }
            }

            double average = sum / a;
            long count = ncr(count1 + count2, count1);
            if (v[n - 1] == lastElement) {
                for (int i = 1; a + i <= b; i++) {
                    count += ncr(count1 + count2, count1 + i);
                }
            }

            out.format("%f%n", average);
            out.println(count);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}